Non-Real Eigenvalues for $\mathcal{PT}$-Symmetric Double Wells
Résumé
We study small, $\mathcal{PT}$-symmetric perturbations of self-adjoint double-well Schrödinger operators in dimension $n\ge 1$. We prove that the eigenvalues stay real for a very small perturbation, then bifurcate to the complex plane as the perturbation gets stronger.